Supporters of a proposed ban on race-based affirmative action said Thursday that they've turned in enough signatures to get the measure on the ballots in Nebraska and Arizona.

But the fight isn't over in either state, with opponents of the ban vowing to challenge the validity of some signatures to the petition that has ignited controversy across the country.

A coalition of opponents based in Michigan filed a lawsuit Monday, accusing Arizona petitioners of committing voter fraud and violating election law by using deceptively worded pitches to convince people to sign.

And a group opposing the measure in Nebraska plans to go to the secretary of state with video and footage that appears to show circulators leaving petitions unattended and filling in information for signers. Both are illegal and could invalidate signatures.

"There's a significant difference between submitted signatures and valid signatures," said David Kramer, head of Nebraskans United, which opposes the measure. "We'll wait to see the outcome of that process before litigation."

But in both states, supporters claim to have gathered far more signatures than needed. In Nebraska, they needed 112,000 and turned in 167,000. In Arizona, organizers needed about 230,000 signatures and submitted nearly 335,000.

The proposed constitutional amendment would bar preferential treatment by public entities on the basis of race, sex, color, ethnicity or national origin.

Supporters say the measure levels the playing field, giving everyone an equal chance at every job. They say most people support the measure and want the chance to vote on it.

Opponents say it plays to people's fears that unqualified minorities are being picked over qualified non-minorities. Affirmative action, they say, ensures good-faith efforts to recruit minority candidates and keep people accountable for their hiring decisions.

Arizona Deputy Secretary of State Kevin Tyne said, barring any legal challenges, his office would have a final tabulation of signatures by late August. In Nebraska, the count of acceptable signatures will be known by mid- to late-August, said Neal Erickson, deputy secretary of state for elections.

Max McPhail, executive director of group pushing the measure in Arizona, scoffed at allegations of wrongdoing. He said Arizona voters will overwhelmingly side with the initiative in November.

"This radical organization believes people should be classified by the government and placed into racial categories and they should be treated differently," McPhail said. "That's the definition of racism."

In Nebraska, the effort was started by a professor at the University of Nebraska-Lincoln who said he saw preferential hiring that infuriated him.

"Nebraskans are speaking loud and clear," Marc Schniederjans said Thursday. "They want the opportunity to end the use of race and gender discrimination and preferences in state employment, contracting and education."

Supporters said they do everything possible to train circulators — both paid and unpaid — to follow the rules. They'll keep gathering signatures in Nebraska on Friday, which is the deadline to turn them in.

The Nebraska and Arizona groups pushing the measure are affiliated with the American Civil Rights Initiative's Super Tuesday for Equal Rights Fund, founded by California businessman and activist Ward Connerly.

Connerly has prevailed three times in past elections, with voters in California, Michigan and Washington approving proposals banning government-sponsored race and gender preferences in public education, state hiring and public contracts.

This year, organizers in Missouri conceded that too few signatures would be gathered by the deadline, and they bowed out in Oklahoma in the face of challenges to the signatures gathered there. A petition drive is still active in Colorado.